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This paper is devoted to work out a stabilized controller by state feedback for a class of nonlinear systems. In this paper, we not only extend the existing results that system has a single power term to the case with multiple coupling power terms, but also consider that the power is time varying, which makes the system studied in this paper more general than that in other literature. By the backstepping method, a linear easy-to-implement controller is designed, which not only ensures the stability of the system but also has a good convergence speed. Finally, with a representative numerical example, by calculating all the parameters in the design procedure, the simulation shows that all the responses of the states and the controller are asymptotically stable at the equilibrium zero, which verifies the effectiveness of the control design scheme of this paper. [ABSTRACT FROM AUTHOR]

Based on the traditional control approach, the position-tracking performance of the teleoperation system with communication delay is generally asymptotically stable. In practical applications, the closed-loop system is expected to achieve stable and finite-time convergence performance. A novel finite-time bilateral control scheme for a telerobotics system with communication delay is presented in this paper. On the basis of the traditional proportional damping injection control, this paper proposes and designs a new finite-time control method by introducing the non-integer power to the position error, velocity, and the combined error with position error and velocity. In comparison to existing proportional damping injection and finite-time control structures, the proposed method not only achieves the finite-time convergence performance of position tracking, but it also has the advantages of a simple structure and fewer gain coefficients. The controller also incorporates the radial basis function (RBF) neural network and adaptive approach to compensate unknown dynamics and external forces, thus also avoiding the measurement of force signals. The Lyapunov–Krasovskii function is then defined, and it is demonstrated that the position tracking of closed-loop teleoperation system has bounded stability and finite-time control performance. The simulation experiment is also performed, and the results further illustrated the bounded stability of the system. Moreover, compared to the position tracking errors of other non-finite-time control methods, it is demonstrated that the proposed finite-time control scheme has a faster convergence rate and higher convergence precision. [ABSTRACT FROM AUTHOR]

Communication delay is an important factor affecting the stability and performance of telerobotic systems. In this paper, a new adaptive proportional damping controller is proposed to improve the stability and performance of the system in the presence of the cases such as asymmetric communication delay, unknown gravity torque, friction torque, and other disturbance torques. The proposed proportional damping control method combines the RBF neural network and adaptive control strategy to compensate for the unknown torque. The stability and robustness of the system are enhanced by adding error-damping items, operator force, and environmental force items. The Lyapunov–Krasovskii functional is employed to analyze and prove the exponential stability and signal boundedness of the closed-loop system. The simulation results verify the correctness of the proposed method, and the comparison with the results of other control methods shows the effectiveness of the designed control strategy. [ABSTRACT FROM AUTHOR]

Summary: This article studies the adaptive control for synchronization of semi‐linear complex spatio‐temporal networks (CSNs). And the leader‐following and leaderless CSN with time‐invariant coupling delay and time‐variant coupling delay are developed separately from two aspects. The adaptive control strategies are proposed to reach the asymptotic convergence of synchronization error. Synchronization criteria and sufficient conditions are obtained for the leader‐following CSN error model and leaderless CSN error model by constructing the apposite Lyapunov–Krasovskii functions and applying Wirtinger's inequality. Finally, two experimental examples are given to verify the feasibility of the theories proposed in this article. [ABSTRACT FROM AUTHOR]